Final answer:
The authoritarian style of parenting is characterized by strict rules, close monitoring, and a lack of warmth, which aligns with the behavior of the parent instructing her child to sit still 'because I said so.'
Step-by-step explanation:
The parenting style observed by the nursing student, where a parent requires unquestioned obedience and issues mandates like 'sit still because I said so,' is most indicative of an authoritarian style of parenting. This style is characterized by strict rule enforcement without much explanation for the rules, close monitoring of children, and a general lack of warmth or affection in the interactions. In contrast, an authoritative parent while also setting clear rules, would provide rationales for them and show more nurturing and warmth. A permissive parent would make few demands and might not set fixed rules for behavior like sitting still. Lastly, an uninvolved parenting style would reflect indifference toward the child's behavior and a lack of rule-setting or active parenting.